This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — Here are the extended sequences based on the patterns identified: 1. Sequence: 1, 2, 3, 5, 6, 7 The pattern of differences is +1, +1, +2, +1, +1. Assuming this pattern of differences (+1, +1, +2) repeats. Step 1: 7 + 2 = 9 Step 2: 9 + 1 = 10 Step 3: 10 + 1 = 11 The extended sequence is: 1, 2, 3, 5, 6, 7, 9, 10, 11 2. Sequence: 5, 2, 4 The pattern of differences is -3, +2. Assuming this pattern repeats. Step 1: 4 - 3 = 1 Step 2: 1 + 2 = 3 Step 3: 3 - 3 = 0 The extended sequence is: 5, 2, 4, 1, 3, 0 3. Sequence (D): 5, 7, 3, 1 The pattern of differences is +2, -4, -2. Assuming this pattern repeats. Step 1: 1 + 2 = 3 Step 2: 3 - 4 = -1 Step 3: -1 - 2 = -3 The extended sequence is: 5, 7, 3, 1, 3, -1, -3 4. Sequence (C): 12, 9, 6, 4, 8 The pattern of operations is -3, -3, -2, +4. Assuming this pattern repeats. Step 1: 8 - 3 = 5 Step 2: 5 - 3 = 2 Step 3: 2 - 2 = 0 Step 4: 0 + 4 = 4 The extended sequence is: 12, 9, 6, 4, 8, 5, 2, 0, 4 5. Sequence (D): 9, 5, 6, 12, 4 The pattern of operations is -4, +1, × 2, ÷ 3. Assuming this pattern repeats. Step 1: 4 - 4 = 0 Step 2: 0 + 1 = 1 Step 3: 1 × 2 = 2 Step 4: 2 ÷ 3 = (2)/(3) The extended sequence is: 9, 5, 6, 12, 4, 0, 1, 2, (2)/(3)